The field of this invention is seismic exploration.
The object of seismic exploration is to obtain an acoustic velocity model of the earth's subsurface from sources and receivers of acoustic energy at the earth's surface. Seismic reflections observed at the surface are generated from boundaries between strata of contrasting acoustic impedances. This invention is concerned with processing conventional seismic reflection observations into a spatial image of the earth consisting of the locations and shapes of the earth's reflecting boundaries and the acoustic velocities (also called `interval velocities`) of the layers between those reflecting boundaries.
The current method of processing seismic reflection data stems from a development of C. H. Dix (Geophysics, Vol. 20, pp. 68-86, 1955) which is based on an earth model consisting of flat layers, as in a cake, whose interval velocities are a function of depth only. Using this layercake earth model, Dix showed that when the offset between source and receiver was increased, the two-way acoustic travel times from source to receiver via the reflectors would increase approximately as two-parameter hyperbolas. The stacking velocity parameters of these hyperbolic moveout relationships between offsets and two-way travel times are directly related to the second derivatives of the hyperbolas at zero offset.
Dix also showed the stacking-velocity parameters were root-mean-square averages of the interval velocities of the layers weighted by their zero-offset travel times. This development provided a general method of inverting seismic data by extrapolation along hyperbolas to zero offset where the stacking velocity parameters could be estimated and inverted into a layercake model of the earth. Empirical verification of the estimated stacking velocity parameters is, however, very difficult, because seismic traces near zero offset are unavailable, and because empirical moveout curves deviate systematically from two-parameter hyperbolas fitted over the entire range of observed offsets. Also, land seismic data need to be refocussed to a flat surface to conform to layercake earth models.
Since Dix's contribution in 1955, seismologists have extended the application of his method of seismic inversion to earth with two- and three-dimensional dipping reflectors between which interval velocities could change laterally. They have also substantially increased multiple coverage of sources and receivers in seismic lines to obtain more reliable estimates of stacking-velocity parameters at zero offset.
Despite the extensions of Dix's method to more complex earth models and the increased multiple coverage of seismic data, current data processing of full-scale seismic data often results in velocity models of the earth which are grossly inaccurate. For this reason, an initial velocity model of the earth is first estimated on the basis of zero-offset seismic measurements. Forward modelling techniques such as raypath tracing and depth migration are then applied to the initial velocity model of the earth to calculate positive-offset travel times which can be compared to those of observed seismic data for possible validation or modification of the earth model.
More recent work has focussed on the use of nonzero-offset velocity measurements and travel times (Gray and Golden, 1983 Society of Exploration Geophysics Convention). The objective of this method was to reduce the error amplification of interval velocity estimates that result from the use of second derivatives at zero offset, embodied in stacking velocity estimates, as opposed to using estimates of first derivatives or slopes of the moveout curves at a nonzero-offset, often called time dips or apparent velocities.
In the work of Gray and Golden, apparent velocities were measured directly from common source and common receiver gathers over the entire range of offsets. This, however, was unsuccessful, for two reasons. Firstly, the measurement of apparent velocities directly from moveout curves of commmon source or receiver gathers is notoriously difficult and cumbersome, as a result of which the measurements were made very sparsely. Secondly, the apparent velocities estimated at a nonzero offset were inaccurate because the entire range of offsets was represented in their measurement, thereby averaging disparate apparent velocities at various offsets in the range. Owing to the sparseness and inaccuracy of the measurements, the inversion of observed seismic data was unsuccessful, as a consequence of which seismologists have abandoned this approach.
The point of departure of this invention from current seismic data processing stems for the poor approximations of two-parameter hyperbolas to the moveout curves of many seismic events over the entire range of offsets of the observed seismic data. For example, geologic anticlines often have elliptical moveout curves where travel times actually decrease as the offsets increase, resulting in imaginary stacking velocities. Consequently, the current practice of stacking such seismic data along two-parameter hyperbolas and extrapolating those results to zero offset eliminates information of many complex geologic structures which are of high interest in seismic exploration. Stacking velocities measured from nonhyperbolic moveout curves are inaccurate, and these errors are highly amplified in calculating interval velocities by Dix's method of seismic inversion. Moreover, unlike random errors, inaccuracies of stacking velocities measured from nonhyperbolic moveout curves are systematic errors which cannot be reduced by increasing multiple coverage of sources and receivers in a seismic line.
This invention teaches how velocity models of the earth can be constructed from observed seismic data by using instantaneous slopes of the moveout curves (called `apparent velocities`) measured over selected ranges of offsets. Nonhyperbolic moveout curves do not prevent apparent velocities from being measured with sufficient accuracy at the average offset of selected ranges of offsets. Moreover, the statistical reliability of measuring such apparent velocities improves as the multiple coverage of sources and receivers is increased. Lastly, the estimates of apparent velocities which are made in the manner of this invention can be empirically verified from the moveout curves of traces in the vicinity of the offset and datum point of the stacked average-offset trace.
The invention provides for apparent velocity measurements at the average offsets of different ranges of observed offsets along the moveout curves. Apparent velocities obtained from each range of offsets can be understood as independent data which travels through distinct regions of the earth with unique trajectories. Therefore, earth models derived from different ranges of offsets may be directly compared, and their congruence serves as a validation of the seismic inversion process. No such validation is possible for current seismic data processing systems because the stacking velocities which they measure are both defined by and dedicated to hyperbolic moveout curves over the entire range from zero offset to the maximum offset of the seismic data.